Video coding using wavelet transform of pixel array formed with motion information

ABSTRACT

A video encoding system and method utilizes a three-dimensional (3-D) wavelet transform and entropy coding that utilize motion information in a way to reduce the sensitivity to motion. In one implementation, the coding process initially estimates motion trajectories of pixels in a video object from frame to frame in a video sequence to account for motion of the video object throughout the frames. After motion estimation, a 3-D wavelet transform is applied in two parts. First, a temporal 1-D wavelet transform is applied to the corresponding pixels along the motion trajectories in a time direction. The temporal wavelet transform produces decomposed frames of temporal wavelet transforms, where the spatial correlation within each frame is well preserved. Second, a spatial 2-D wavelet transform is applied to all frames containing the temporal wavelet coefficients. The wavelet transforms produce coefficients within different sub-bands. The process then codes wavelet coefficients. In particular, the coefficients are assigned various contexts based on the significance of neighboring samples in previous, current, and next frame, thereby taking advantage of any motion information between frames. The wavelet coefficients are coded independently for each sub-band to permit easy separation at a decoder, making resolution scalability and temporal scalability natural and easy. During the coding, bits are allocated among sub-bands according to a technique that optimizes rate-distortion characteristics.

RELATED APPLICATION(S)

This is a divisional of U.S. patent application Ser. No. 09/599,160,entitled “Video Coding System and Method Using 3-D Discrete WaveletTransform and Entropy Coding With Motion Information”, which was filedJun. 21, 2000, and is assigned to Microsoft Corporation.

TECHNICAL FIELD

This invention relates to systems and methods for video coding. Moreparticularly, this invention relates to systems and methods that employwavelet transforms for video coding.

BACKGROUND

Efficient and reliable delivery of video data is becoming increasinglyimportant as the Internet continues to grow in popularity. Video is veryappealing because it offers a much richer user experience than staticimages and text. It is more interesting, for example, to watch a videoclip of a winning touchdown or a Presidential speech than it is to readabout the event in stark print.

With the explosive growth of the Internet and fast advance in hardwaretechnologies and software developments, many new multimedia applicationsare emerging rapidly. Although the storage capability of the digitaldevices and the bandwidth of the networks are increasing rapidly, videocompression still plays an essential role in these applications due tothe exponential growth of the multimedia contents both for leisure andat work. Compressing video data prior to delivery reduces the amount ofdata actually being transferred over the network. Image quality is lostas a result of the compression, but such loss is generally tolerated asnecessary to achieve acceptable transfer speeds. In some cases, the lossof quality may not even be detectable to the viewer.

Many emerging applications require not only high compression efficiencyfrom the various coding techniques, but also greater functionality andflexibility. For example, in order to facilitate contend-based mediaprocessing, retrieval and indexing, and to support user interaction,object-based video coding is desired. To enable video delivery overheterogeneous networks (e.g., the Internet) and wireless channels, errorresilience and bit-rate scalability are required. To produce a codedvideo bitstream that can be used by all types of digital devices,regardless their computational, display and memory capabilities, bothresolution scalability and temporal scalability are needed.

One common type of video compression is the motion-compensation-basedvideo coding scheme, which is employed in essentially all compressionstandards such as MPEG-1, MPEG-2, MPEG-4, H.261, and H.263. Such videocompression schemes use predictive approaches that encode information toenable motion prediction from one video frame to the next.

Unfortunately, these conventional motion-compensation-based codingsystems, primarily targeted for high compression, fail to provide newfunctionalities such as scalability and error robustness. The recentMPEG-4 standard adopts an object-based video coding scheme to enableuser interaction and content manipulation, but the scalability of MPEG-4is very limited. Previously reported experiments with MPEG-2, MPEG-4,and H.263 indicate that the coding efficiency generally loses 0.5-1.5 dBwith every layer, compared with a monolithic (non-layered) codingscheme. See, for example, B. G. Haskell, A. Puri and A. N. Netravali,Digital Video: An Introduction to MPEG-2, Chapman & Hall, New York,1997; and L. Yang, F. C. M. Martins, and T. R. Gardos, “Improving H.263+Scalability Performance for Very Low Bit Rate Applications,” In Proc.Visual Communications and Image Processing, San Jose, Calif., January1999, SPIE.

Since these standard coders are all based on a predictive structure, itis difficult for the coding schemes to achieve efficient scalability dueto the drift problem associated with predictive coding. Currently, thereare proposals for MPEG-4 streaming video profile on fine granularityscalable video coding. However, these proposals are limited to provideflexible rate scalability only and the coding efficiency is still muchlower than that of non-layered coding schemes.

An alternative to predictive-based video coding schemes is threedimensional (3-D) wavelet video coding. One advantage of 3-D waveletcoding over predictive video coding schemes is the scalability(including rate, PSNR, spatial, and temporal), which facilitates videodelivery over heterogeneous networks (e.g., the Internet) and futurewireless video services. However, conventional 3-D wavelet coding doesnot use motion information that is proven to be very effective inpredictive coders in terms of removing temporal redundancy. Although thecomputationally intensive motion estimation is avoided, the performanceof 3D wavelet video coding remains very sensitive to the motion. Withoutmotion information, motion blur occurs due to a temporal averagingeffect of several frames. In addition, most 3-D wavelet video coders donot support object-based functionality, which is needed in the nextgeneration multimedia applications.

Accordingly, there is a need for an efficient 3-D wavelet transform forvideo coding that employs motion information to reduce the sensitivityto motion and remove the motion blur in the resulting video playback.Additionally, an improved 3-D wavelet transform should supportobject-based functionality.

SUMMARY

A video encoding system and method utilizes a three-dimensional (3-D)wavelet transform and entropy coding that utilize motion information ina way to reduce the sensitivity to motion and remove any motion blur inthe resulting video playback.

In one implementation, the video encoding process initially estimatesmotion trajectories of pixels in a video object from frame to frame in avideo sequence. The motion estimation accounts for motion of the videoobject throughout the frames, effectively aligning the pixels in thetime direction. The motion estimation may be accomplished by matchingcorresponding pixels in the video object from frame to frame.

After motion estimation, a 3-D wavelet transform is applied in twoparts. First, a temporal 1-D wavelet transform is applied to thecorresponding pixels along the motion trajectories in a time direction.The temporal wavelet transform produces decomposed frames of temporalwavelet transforms, where the spatial correlation within each frame iswell preserved. Second, a spatial 2-D wavelet transform is applied toall frames containing the temporal wavelet coefficients. The wavelettransforms produce coefficients within different sub-bands.

The process then codes wavelet coefficients. In particular, thecoefficients are assigned various contexts based on the significance ofneighboring samples in previous, current, and next frame, thereby takingadvantage of any motion information between frames. The waveletcoefficients are coded independently for each sub-band to permit easyseparation at a decoder, making resolution scalability and temporalscalability natural and easy. During the coding, bits are allocatedamong sub-bands according to a technique that optimizes rate-distortioncharacteristics. In one implementation, the number of bits are truncatedat points in a rate-distortion curve that approximates a convex hull ofthe curve.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a video distribution system, including avideo encoder at a content producer/provider and a video decoder at aclient.

FIG. 2 is a flow diagram of a video coding process usingthree-dimensional shape-adaptive discrete wavelet transforms and motionestimation information.

FIG. 3 illustrates four frames in a video sequence to demonstratemotions estimation of pixels from frame to frame.

FIG. 4 illustrates two consecutive frames and demonstrates a case wherea pixel continues from one frame to the next.

FIG. 5 illustrates two consecutive frames and demonstrates a case wherea pixel terminates in a current frame and does not continue to the nextframe.

FIG. 6 illustrates two consecutive frames and demonstrates a case wherea pixel emerges in the next frame, but does not appear in the currentframe.

FIG. 7 illustrates two consecutive frames and demonstrates a case whereto pixels in the current frame collide at one pixel in the next frame.

FIG. 8 is a flow diagram of a 3-D wavelet transform process applied tovideo frames.

FIG. 9 illustrates sub-bands within a video frame that are formed by thewavelet transform.

FIG. 10 is a flow diagram of a sub-band encoding process.

FIG. 11 illustrates three frames to demonstrate how a context for apixel is determined in terms of neighboring pixels.

FIG. 12 is a flow diagram of a bitstream construction and truncationprocess.

FIG. 13 illustrates a rate-distortion curve that is used in the FIG. 12process.

DETAILED DESCRIPTION

This disclosure describes a video coding scheme that utilizes athree-dimensional (3-D) wavelet transform and coding scheme that issuitable for object-based video coding. The 3-D wavelet transform usesmotion trajectories in the temporal direction to obtain more efficientwavelet decomposition and to reduce or remove the motion blurringartifacts for low bit-rate coding.

The 3-D wavelet transformation produces coefficients within differentsub-bands. An entropy coder is employed to code each sub-bandindependently in a manner that takes advantage of the motioninformation. The entropy coder also uses rate-distortion curves tooptimize the bit-allocation among sub-bands. Given these attributes, theentropy coder process may be referred to as “Embedded Sub-band Codingwith Optimized Truncation” (or short handedly as “ESCOT”). The entropycoder outputs independent embedded bitstreams for each sub-band thatmeet scalability requirements of new multimedia applications.

Accordingly, unlike conventional 3-D wavelet coding schemes, motioninformation is used for both 3-D shape adaptive wavelet transforms andthe entropy coding. The proposed coding scheme has comparable codingefficiency with MPEG4, while having more functionalities andflexibility, such as, flexible rate scalability, spatial scalability,and temporal scalability. This makes the coding scheme very suitable fornumerous applications like video streaming, interactive multimediaapplications, and video transmission over wireless channels.

The coding scheme is described in the context of delivering video dataover a network, such as the Internet or a wireless network. However, thevideo coding scheme has general applicability to a wide variety ofenvironments.

Exemplary System Architecture

FIG. 1 shows a video distribution system 100 in which a contentproducer/provider 102 produces and/or distributes video over a network104 to a client 106. The network 104 is representative of many differenttypes of networks, including cable, the Internet, a LAN (local areanetwork), a WAN (wide area network), a SAN (storage area network), andwireless networks (e.g., satellite, cellular, RF, microwave, etc.).

The content producer/provider 102 may be implemented in many ways,including as one or more server computers configured to store, process,and distribute video data. The content producer/provider 102 has a videostorage 110 to store digital video files 112 and a distribution server114 to encode the video data and distribute it over the network 104. Theserver 104 has one or more processors 120, an operating system 122(e.g., Windows NT, Unix, etc.), and a video encoder 124. The videoencoder 124 may be implemented in software, firmware, and/or hardware.The encoder is shown as a separate standalone module for discussionpurposes, but may be constructed as part of the processor 120 orincorporated into operating system 122 or other applications (notshown).

The video encoder 124 encodes the video data stored as files 112 using a3-D wavelet transformer 130 and codes the resulting coefficients usingan entropy coder 132. In one implementation, the 3-D wavelet transformer130 implements a shape-adaptive discrete wavelet transform (SA-DWT),which is an efficient wavelet transform for arbitrarily shaped visualobjects. With SA-DWT, the number of coefficients after SA-DWT isidentical to the number of pixels in an original arbitrarily shapedvisual object. In addition, SA-DWT preserves the spatial correlation,locality properties of wavelet transforms, and self-similarity acrosssub-bands. It is noted, however, that aspects of this invention may beimplemented using other types of wavelet transforms.

The video encoder 124 utilizes motion information in the temporaldirection of the video sequence. A motion trajectory for each pixelinside a video object is traced from frame-to-frame using one of avariety of motion estimation processes. Then, a one-dimensional (1-D)SA-DWT is performed along each motion trajectory in the time directionto produce temporally decomposed frames of wavelet coefficients. Aftertemporal decomposition, a spatial two-dimensional (2-D) SA-DWT isapplied to all temporally decomposed frames.

The 3-D (i.e., 1-D temporal and 2-D spatial) wavelet transform solvestwo problems. First, it can handle arbitrarily shaped video objectswhile having flexible bit-rate, spatial, and temporal scalabilities asin most wavelet-based coding schemes. Secondly, the 3-D wavelettransform tracks the video object motion and performs the wavelettransform among corresponding pixels for that object while keeping thespatial correlation within a frame. Thus, it will efficiently decomposethe video-object sequence and more efficient compression is feasible.

After the wavelet transform, the entropy coder 132 codes thecoefficients of each sub-band independently. The coder assigns variouscontexts to the coefficients based on data regarding neighboring samplesin the previous, current, and next frames. This context assignment thustakes advantage of the motion information between frames. The codedbitstreams for each sub-band are subsequently combined to form a finalbitstream that satisfies scalability requirements. In oneimplementation, the coded bitstreams are combined using a multi-layerbitstream construction technique.

The client 106 may be embodied in many different ways, including as acomputer, a handheld device, a set-top box, a television, a gameconsole, information appliance, wireless communication device, and soforth. The client 106 is equipped with a processor 140, a memory 142,and one or more media output devices 144. The memory 142 stores anoperating system 150 (e.g., a Windows-brand operating system) thatexecutes on the processor 140.

The operating system 150 implements a client-side video decoder 152 todecode the video stream. The decoder employs an inverse wavelettransformer 154 to decode the video stream. Following decoding, theclient stores the video in memory 142 and/or plays the video via themedia output devices 144.

Coding Process

FIG. 2 shows a video coding process 200 for coding video objects. Theprocess 200 may be implemented, for example, by the video encoder 124 inthe content producer/provider 102. The process may be implemented ascomputer-readable instructions stored in a computer-readable medium(e.g., memory, transmission medium, etc.) that, when executed, performthe operations illustrated as blocks in FIG. 2.

At block 202, the video encoder estimates motion trajectories of pixelsin a video object from frame to frame in a video sequence to account formotion of the video object throughout the frames. In one implementation,the video encoder uses a pixel matching process to match correspondingpixels from frame-to-frame in the temporal direction. The matchingoperation traces motion trajectories for the corresponding pixels,thereby aligning the pixels in the temporal direction. It is noted thatother motion estimation schemes may be used instead of the pixelmatching process.

At block 204, the video encoder uses the wavelet transformer 130 toperform a wavelet transform on the corresponding pixels in the timedimension along the motion trajectories. In one implementation, thetransformer uses a temporal 1-D shape-adaptive discrete wavelettransform (SA-DWT) for the corresponding pixels. The temporal wavelettransform produces decomposed frames of temporal wavelet transforms,where the spatial correlation within each frame is well preserved.

At block 206, the wavelet transformer 130 applies a spatial 2-Dshape-adaptive discrete wavelet transform for all frames containing thetemporal wavelet coefficients (block 206). The wavelet transformsproduce coefficients within different sub-bands. The 3-D SA-DWTs ofblocks 204 and 206 are explored in more detail below under the heading“3-D SA-DWT (Blocks 204 and 206)”.

At block 208, the entropy coder 132 codes the wavelet coefficientsindependently for each sub-band and optimizes the bits allocated to eachsub-band. The entropy coder 132 outputs a bitstream of independentlycoded sub-bands. The entropy encoding operation is described below inmore detail under the heading “ESCOT (Block 208)”.

3-D SA-DWT (Blocks 204 and 206)

As shown in operation 202 of FIG. 2, the video encoder initiallyconstructs a 1-D array of corresponding pixels obtained from motionestimation (e.g., pixel-matching scheme) to identify correspondingpixels from frame to frame. The motion estimation aligns the pixels thetemporal direction.

FIG. 3 shows four frames 300, 302, 304, and 306 plotted along the timedimension. Each frame has a video object 310 in the form of a “smileyface” that moves from frame to frame. Consider a pixel “p” used to forman eye in the smiley face object 310. The first task prior totransformation is to match the pixel p in each frame to account formotion of the object. The corresponding pixels from frame-to-frame arelinked by line 312.

After the 1-D array of corresponding pixels is built, the wavelettransformer 130 at content provider 102 performs a temporaldecomposition along the motion trajectories. More specifically, thetransformer 130 applies a 1-D shape-adaptive discrete wavelet transformto the 1-D array to obtain a 1-D coefficient array. The coefficients inthe 1-D array are then redistributed to their corresponding spatialposition in each frame.

A video object normally is not limited to 2-D translation movementwithin a frame, but may move in/out or zoom in/out of a video scene anytime. This gives rise to four separate cases of pixel transitions fromframe to frame.

-   Case 1: Continuing pixels. This is the normal case as pixels    continue in one-to-one correspondence between two consecutive    frames. In this case, the temporal 1-D pixel array is extended to    include the corresponding pixel from the next frame. FIG. 4    illustrates the continuing pixel case, where a pixel p continues    from one frame n to a next frame n+1.-   Case 2: Terminating pixels. This case represents pixels that do not    carry to the next frame, and hence no corresponding pixels can be    found in the next frame. In this case, the temporal 1-D pixel array    is ended at the terminating pixel. FIG. 5 illustrates the    terminating pixel case, where a pixel p ends in frame n and cannot    be found in the next frame n+1.-   Case 3: Emerging pixels. This case represents pixels that originate    in the next frame and have no corresponding pixels in the previous    frame. In this case, the emerging pixel will start a new temporal    1-D pixel array. FIG. 6 illustrates the emerging pixels case, where    a new pixel p originates in frame n+1 and has no corresponding pixel    in preceding frame n.-   Case 4: Colliding pixels. This case represents pixels that have more    than one corresponding pixel in a previous frame. In this case, the    colliding pixel will be assigned to only one of the corresponding    pixels in the previous frame, and all the other corresponding pixels    are marked as terminating pixels. FIG. 7 illustrates the colliding    pixels case, where pixels p₁ and p₂ in frame n both correspond to a    pixel in next frame n+1. Here, pixel p₁ is designated as a    terminating pixel, thereby ending the 1-D pixel array containing    that pixel. Pixel p₂ is a continuing pixel that is added to the    ongoing 1 -D pixel array for that pixel.

FIG. 8 shows the 3-D wavelet transformation process 800 for a videosequence. The process 800 may be implemented by the wavelet transformer130 at the video encoder 124. The operations depicted as blocks may beembodied as computer-executable instructions embodied on computerreadable media (e.g., storage media, communications media, etc.).

Given a group of pictures/frames F_(i), for i=0, . . . , N−1, it isassumed that the motion of each pixel with reference to the next framehas been obtained using a motion estimation, for example, a block-basedmotion estimation algorithm. For each block in frame i that containspixels from the video object, a search for the best-matched block inframe i+1 is made and the motion vector for that block is estimated. Forpurposes of 3-D SA-DWT, the motion vector of every pixel within a blockis set to the same as that of the block. Other motion estimationtechniques may be used.

After motion estimation, each pixel in the current frame may representone of the four cases described above: continuing pixels, terminatingpixels, emerging pixels, and colliding pixels. Additionally, all pixelsin the last frame F_(N−1) are terminating pixels since there is no“next” frame. For discussion purposes, assume that the wavelettransformer 130 employs odd-symmetric bi-orthogonal wavelet filters,although other types of wavelet filters can also be used.

At block 802, the transformer 130 initializes the 3-D shape-adaptivediscrete wavelet transform. In our example, counter value “i” is set to0 and all pixels within an object boundary in all N frames are marked asUNSCANNED.

At block 804, the wavelet transformer 130 performs 1-D temporal SA-DWTon the frames. This operation includes constructing temporal 1-D pixelarrays, transforming those arrays to produce low-pass (LP) and high-pass(HP) coefficients, and organizing LP and HP coefficients into low-passand high-pass frames.

One preferred implementation of the 1-D temporal SA-DWT is illustratedas blocks 804(1)-804(12). The transform operation (block 804) loopsthrough every pixel in every frame of the video sequence. Block 804(1)represents this iterative process as being for every pixelp_(i)(x_(i),y_(i)) within object boundary in frame F_(i). At block804(2), the pixel is examined to see if it is marked as UNSCANNED. Ifnot, the pixel has already been considered and the process proceeds tothe next pixel at block 804(1). Otherwise, assuming the pixel is stillmarked UNSCANNED (i.e., the “yes” branch from block 804(2)), the pixelbecomes the first pixel of a new temporal 1-D pixel array (block804(3)). Essentially, this pixel represents the emerging pixel casewhere it is the first pixel to originate in a frame.

The inner loop of operations consisting of blocks 804(4)-804(9) evaluatewhether the pixels are continuing pixels, thereby growing the pixelarray, or terminating pixels that end the array. At block 804(4), thepixel is evaluated to determine whether it is a terminating pixel,meaning that there is no corresponding pixel in the next frame.Introducing “j” as a new counter equal to “i”, if pixelp_(j)(x_(j),y_(j)) is a terminating pixel, it is the last pixel in thetemporal 1-D array and hence the array is ready for transformation atblock 804(9) (described below).

Conversely, if pixel p_(j)(x_(j),y_(j)) is not a terminating pixel(i.e., the “no” branch from block 804(4)), the process evaluates whetherthe corresponding pixel p_(j+1)(x_(j+1), y_(j+1)) in frame F_(j+1) ismarked as UNSCANNED, where (x_(j+1), y_(j+1))=(x+mv_(x), y+mv_(y)) and(mv_(x), mv_(y)) is the motion vector from pixel p_(j)(x_(j),y_(j)) inframe F_(j) to its corresponding pixel p_(j+1)(x_(j+1), y_(j+1)) inframe F_(j+1) (block 804(5)). If the corresponding pixelp_(j+1)(x_(j+1), y_(j+1)) is UNSCANNED (i.e., the “yes” branch fromblock 804(5)), the corresponding pixel p_(j+1)(x_(j+1), y_(j+1)) isadded as the next pixel in the 1-D pixel array (block 804(6)). Thissituation represents the continuing pixel case (FIG. 4) in whichconsecutive pixels are added to the temporal 1-D array. Thecorresponding pixel p_(j+1)(x_(j+1), y_(j+1)) is then marked as SCANNEDto signify that it has been considered (block 804(7)). Process continueswith consideration of the next corresponding pixel p_(j+2)(x_(j+2),y_(j+2)) in the next frame F_(j+2) (block 802(8)).

On the other hand, as indicated by the “no” branch from block 804(5),the corresponding pixel p_(j+1)(x_(j+1), y_(j+1)) may have already beenmarked as SCANNED, indicating that this pixel also corresponded to atleast one other pixel that has already been evaluated. This representsthe colliding pixel case illustrated in FIG. 7. In this case, thesubject pixel p_(j)(x_(j),y_(j)) in frame F_(j) will terminate the 1-Dpixel array (block 804(9)).

At block 802(10), the transformer applies 1-D arbitrary length waveletfiltering to each terminated 1-D pixel array. This operation yields atransformed low-pass thread of coefficients L_(k)(x_(k),y_(k)), k=i, . .. , j−1, and a transformed high-pass thread of coefficientsH_(k)(x_(k),y_(k)), k=i, . . . , j−1. The low-pass coefficientsL_(k)(x_(k),y_(k)) are organized into a low-pass frame k at position(x_(k),y_(k)) and the high-pass coefficients H_(k)(x_(k),y_(k)) areorganized into a high-pass frame k at position (x_(k),y_(k)). Isolatedpixels can be scaled by a factor (e.g., square root of 2) and put backinto their corresponding positions in both low-pass and high-passframes.

At block 804(11), the process evaluates whether this is the last frame.If not, the process continues with the next frame F_(i+1) (block804(12)).

At block 806, the low-pass frames are sub-sampled at even frames toobtain temporal low-pass frames and the high-pass frames are sub-sampledat odd frames to obtain temporal high-pass frames. If more temporaldecomposition levels are desired (i.e., the “yes” branch from block808), the operations of blocks 802-806 are repeated for the low-passframes. Note that the motion vectors from frame F_(k) to F_(k+2) can beobtained by adding the motion vectors from F_(k) to F_(k+1) and F_(k+1)to F_(k+2).

Following the temporal transform, at block 810, the transformer 130performs spatial 2-D SA-DWT transforms according to the spatial shapesfor every temporally transformed frame. This is essentially the sameoperation illustrated as block 206 in FIG. 2.

ESCOT (Block 208)

After wavelet transformation, the resulting wavelet coefficients arecoded using a powerful and flexible entropy coding process called ESCOT(Embedded Sub-band Coding with Optimized Truncation) that uses motioninformation. The entropy coding technique used in ESCOT is similar tothe EBCOT (Embedded Block Coding with Optimized Truncation) for stillimages, which was adopted in JPEG-2000. However, unlike EBCOT, the ESCOTcoding scheme is designed for video content and employs a set of codingcontexts that make it very suitable for scalable video objectcompression and the 3D SA-DWT described above, and that take intoaccount motion information between frames. The ESCOT coding scheme isimplemented, for example, by the entropy coder 132 of video encoder 124(FIG. 1).

The ESCOT coding scheme can be characterized as two main stages: (1)sub-band or entropy coding and (2) bitstream construction. These twostages are described separately below.

Stage 1: Sub-Band Coding

As explained above, the 3-D wavelet transform produces multiplesub-bands of wavelet coefficients. The spatial 2-D wavelet transformdecomposes a frame in the horizontal direction and in the verticaldirection to produce four sub-bands: a low-low (LL) sub-band, a high-low(HL) sub-band, a low-high (LH) sub-band, and a high-high (HH) sub-band.FIG. 9 shows the four sub-bands from the spatial 2-D wavelet transform.The LL sub-band typically contains the most interesting information. Itcan be decomposed a second time to produce sub-sub-bands within the LLsub-band, as depicted by bands LL2, LH2, HL2, and HH2.

The ESCOT coding scheme codes each sub-band independently. This isadvantageous in that each sub-band can be decoded independently toachieve flexible spatial and temporal scalabilities. A user can mixarbitrary number of spatio-temporal sub-bands in any order to obtain thedesired spatial and temporal resolution. Another advantage is thatrate-distortion optimization can be done among sub-bands, which mayimprove compression efficiency.

FIG. 10 shows the sub-band coding process 1000, which is implemented bythe entropy coder 132. The process may be implemented ascomputer-readable instructions that, when executed, perform theoperations identified in the sub-band coding process 1000.

At block 1002, the number of contexts used in the coding is reduced byexploiting the symmetric property of wavelet sub-bands throughtransposition of selected sub-bands. Transposing allows certainsub-bands to share the same context. For example, the LLH sub-band, HLLsub-band, and LHL sub-band that are produced from the 3-D transform canshare the same contexts and coding scheme if the HLL and LHL sub-bandsare transposed to have the same orientation as the LLH sub-band beforeencoding. After sub-band transposition, four classes of sub-bandsremain: LLL, LLH, LHH and HHH.

At block 1004, for each sub-band, the quantized coefficients are codedbit-plane by bit-plane. In a given bit-plane, different codingprimitives are used to code a sample's information of this bit-plane.The coding primitives take into account motion information by examiningneighboring samples in previous, current, and next frames anddetermining the significant of these neighboring samples.

In one implementation, there are three coding primitives: zero coding(ZC), sign coding (SC) and magnitude refinement (MR). The zero and signcoding primitives are used to code new information for a single samplethat is not yet significant in the current bit-plane. Magnituderefinement is used to code new information of a sample that is alreadysignificant. Let σ[i,j,k] be a binary-valued state variable, whichdenotes the significance of the sample at position [i,j,k] in thetransposed sub-band. The variable σ[i,j,k] is initialized to 0 andtoggled to 1 when the corresponding sample's first non-zero bit-planevalue is coded. Additionally, a variable χ[i,j,k] is defined as the signof that sample, which is 0 when the sample is positive and 1 when thesample is negative.

Zero Coding: When a sample is not yet significant in the previousbit-plane, i.e. σ[i,j,k]=0, this primitive operation is used to code thenew information about the sample. It tells whether the sample becomessignificant or not in the current bit-plane. The zero coding operationuses the information of the current sample's neighbors as the context tocode the current sample's significance information.

More specifically, the zero coding operation evaluates four categoriesof a sample's neighbors:

-   -   1. Immediate horizontal neighbors. The number of horizontal        neighbors that are significant are denoted by the variable “h”,        where 0<h<2.    -   2. Immediate vertical neighbors. The number of vertical        neighbors that are significant are denoted by the variable “v”,        where 0<v<2.    -   3. Immediate temporal neighbors. The number of temporal        neighbors that are significant are denoted by the variable “a”,        where 0<a<2.    -   4. Immediate diagonal neighbors. The number of diagonal        neighbors that are significant are denoted by the variable “d”,        where 0<d<12.

FIG. 11 shows the four categories of neighbors in three consecutiveframes 1100, 1102, and 1104. A current sample “s” resides in the middleframe 1102. Two horizontal neighbors “h” reside immediately adjacent tothe sample “s” in the middle frame 1102. Two vertical neighbors “v”reside immediately above and below the sample “s” in the middle frame1102. Two temporal neighbors “a” reside immediately before and after thesample “s” in the previous and following frames 1100 and 1104. Twelvepossible diagonal neighbors “d” reside diagonally from the sample “s” inall three frames 1100, 1102, and 1104.

It is noted that the temporal neighbors “a” of the sample are notdefined as the samples that have the same spatial positions in theprevious and next frames. Rather, two samples in consecutive frames aredeemed to be temporal neighbors when they are in the same motiontrajectory. That is, the temporal neighbors are linked by the motionvectors, as illustrated by vectors 1110 and 1112 in FIG. 11.

Coding efficiency is improved because there is more correlation alongthe motion direction. The motion vector for a sample in a high levelsub-band can be derived from the motion vectors in the low levelsub-bands. In spatial decomposition, for example, motion vectors aredown-sampled when the wavelet coefficients are down-sampled. Because therange and resolution of the sub-bands are half of the originalsub-bands, the magnitude of the motion vectors are divided by two torepresent the motion of the samples in that sub-band. If a sample has nocorrespondent motion vector, a zero motion vector is assigned to thesample.

An exemplary context assignment map for zero coding of the foursub-bands is listed in Tables 1-3. If the conditions of two or more rowsare satisfied simultaneously, the lowest-numbered context is selected.An adaptive context-based arithmetic coder is used to code thesignificance symbols of the zero coding. TABLES 1-3 Exemplary ContextAssignment map for Zero Coding LLL and LLH Sub-bands LHH Sub-band h v ad Context h v + a d Context 2 x x x 0 2 x x 0 1 ≧1 x x 0 1 ≧3 x 0 1 0 ≧1x 1 1 ≧1 ≧4 1 1 0 0 x 2 1 ≧1 x 2 0 2 0 x 3 1 0 ≧4 3 0 1 0 x 4 1 0 x 4 00 ≧1 x 5 0 ≧3 x 5 0 0 0 3 6 0 ≧1 ≧4 6 0 0 0 2 7 0 ≧1 x 7 0 0 0 1 8 0 0≧4 8 0 0 0 0 9 0 0 x 9 HHH Sub-band d h + v + a Context ≧6 x 0 ≧4 ≧3 1≧4 x 2 ≧2 ≧4 3 ≧2 ≧2 4 ≧2 x 5 ≧0 ≧4 6 ≧0 ≧2 7 ≧0 1 8 ≧0 0 9

Sign Coding: Once a sample becomes significant in the current bit-plane,the sign coding operation is called to code the sign of the significantsample. Sign coding utilizes an adaptive context-based arithmetic coderto compress the sign symbols. Three quantities for the temporalneighbors “a”, the vertical neighbors “v”, and the horizontal neighbors“h” are defined as follows:h=min{1, max{−1, σ[i−1,j,k].(1−2χ[i−1,j,k])+σ[i+1,j,k].(1−2χ[i+1,j,k])}}v=min{1, max{−1, σ[i,j−1,k].(1−2χ[i,j−1,k])+σ[i,j+1,k].(1−2χ[i,j+1,k])}}a=min{1, max{−1, σ[i,j,k−1].(1−2χ[i,j,k−1])+σ[i,j,k+1].(1−2χ[i,j,k+1])}}

The symbol {circumflex over (χ)} means the sign symbol prediction in agiven context. The symbol sent to the arithmetic coder is {circumflexover (χ)} XOR χ. An exemplary context assignment map for sign coding ofthe four sub-bands is provided in Tables 4-6. TABLES 4-6 ExemplaryContext Assignment map for Sign Coding h = −1 H = 0 v a {circumflex over(χ)} Context v a {circumflex over (χ)} Context −1 −1 0 0 −1 −1 0 9 −1 00 1 −1 0 0 10 −1 1 0 2 −1 1 0 11   0 −1 0 3 0 −1 0 12   0 0 0 4 0 0 0 13  0 1 0 5 0 1 1 12   1 −1 0 6 1 −1 1 11   1 0 0 7 1 0 1 10   1 1 0 8 1 11 9 h = 1 v a {circumflex over (χ)} Context −1 −1 1 8 −1 0 1 7 −1 1 1 6  0 −1 1 5   0 0 1 4   0 1 1 3   1 −1 1 2   1 0 1 1   1 1 1 0

Magnitude Refinement: Magnitude refinement is used to code any newinformation of a sample that has already become significant in theprevious bit-plane. This operation has three possible contexts: 0, 1, or2. The context is 0 if the magnitude refinement operation is not yetused in the sample. The context is 1 if the magnitude refinementoperation has been used in the sample and the sample has at least onesignificant neighbor. Otherwise, the context is 2.

Using the three coding primitive operations—zero coding, sign coding,and magnitude refinement—a sub-band coefficient can be coded withoutloss. One preferred implementation of the coding operation 1004 isillustrated in FIG. 10 as blocks 1004(1)-1004(6).

At block 1004(1) in FIG. 10, a significant map is initialized toindicate that all samples are insignificant. As an example, a binaryvalue “1” represents that a sample is significant and a binary value “0”represents that a sample is insignificant. Accordingly, followinginitialization, the significant map contains all zeros.

Then, for each bit-plane and beginning with the most significantbit-plane, the coding procedure makes three consecutive passes. Eachpass processes a “fractional bit-plane”. The reason for introducingmultiple coding passes is to ensure that each sub-band has a finelyembedded bitstream. By separating zero coding and magnitude refinementinto different passes, it is convenient to design efficient andmeaningful context assignment. In each pass, the scanning order is alongi-direction firstly, then j-direction, and k-direction lastly.

At block 1004(2), a significant propagation pass is performed. This passprocesses samples that are not yet significant but have a “preferredneighborhood”, meaning that the sample has at least a significantimmediate diagonal neighbor for the HHH sub-band, or at least asignificant horizontal, vertical, or temporal neighbor for the othersub-bands. If a sample satisfies these conditions, the zero codingprimitive is applied to code the symbol of the current bit-plane forthis sample. If the sample becomes significant in the current bit-plane,the sign coding primitive is used to code the sign.

At block 1004(3), a magnitude refinement pass is performed to code thosesamples that are already deemed to be significant. The symbols of thesesamples in the current bit-plane are coded by the magnitude refinementprimitive given above.

At block 1004(4), a normalization pass is performed to code thosesamples that are not yet coded in the previous two passes. These samplesare considered insignificant, so zero coding and sign coding primitivesare applied in the normalization pass.

At block 1004(5), the significant map is updated according to thepasses. The updated map reflects the change to those samples that weremarked as significant during the passes. Once a sample is identified assignificant, it remains significant. This process is then repeated foreach bit plane until the least significant bit plane has been coded, asrepresented by blocks 1004(6) and 1004(7).

Stage 2: Bitstream Construction

In the previous stage of sub-band entropy coding, a bitstream is formedfor each sub-band. In the 2D realm, there are seven bitstreams; in the3-D realm, there are fifteen bitstreams. Afterwards, in the currentstage, a final bitstream is constructed by truncating and multiplexingthe sub-band bitstreams. The goal is to produce a final bitstream thatcontains the most effective, yet fewest number, of bits to reduce theamount of data being sent over the network to the receiving client. Thebitstream construction takes in consideration that not all decoders willhave the same capabilities to decode video. The issue thus becomes howto determine where a bitstream should be truncated and how to multiplexthe bitstreams to achieve more functionality (e.g., better PSNRscalability and resolution scalability).

FIG. 12 shows an optimal bitstream truncation and construction procedure1200, which may be implemented by the entropy coder 132 of the videoencoder 124 (FIG. 1). At block 1202, the entropy coder truncates eachsub-band bitstream using rate distortion optimization. Given a specificbit-rate R_(max), a bitstream can be constructed that satisfies thebit-rate constraint and with minimal distortion. One candidatetruncation point is the end of each entropy coding pass. At the end ofeach pass, the bit length and the distortion reduction is calculated anda value for each candidate truncation point can be plotted to produce anapproximate R-D (rate-distortion) curve.

FIG. 13 shows an exemplary R-D curve 1300 formed by five candidatetruncation points 1302.

The entropy coder locates the convex hull of the R-D curve, andtruncation is performed on those candidate truncation points that resideat the convex hull of R-D curve. This guarantees that at everytruncation point, the bitstream is rate-distortion optimized. Given arate-distortion slope threshold λ, one can find truncation points of asub-band where the rate-distortion slope is greater than λ. To satisfythe bit-rate constraint and to make the distortion minimal, the smallestvalue of λ such that R_(λ)≦R_(max) is chosen. One suitable algorithm forfinding such a threshold can be found in D. Taubman (editor), “JPEG2000Verification Model: Version VM4.1,” ISO/IEC JTC 1/SC 29/WG1 N1286.

At block 1204, the entropy coder employs a multi-layer bitstreamconstruction technique to form a final multi-layer bitstream containinga quality level's data. To make a N-layer bitstream, a set of thresholdsλ₁>λ₂> . . . >λ_(N) that satisfy R_(λ) _(N) ≦R_(max) are selected. Withevery threshold, a truncation point is found and a layer of bitstreamfrom each sub-band is obtained. The corresponding layers from all thesub-bands constitute the layers of the final bitstream.

The bitstream construction process offers many advantages in terms ofquality scalability, resolution scalability, temporal scalability, andother forms of scalability. The multi-layer bitstream promotes qualityscalability in that the client-side decoder 152, depending uponavailable bandwidth and computation capability, can select one or morelayers to be decoded. The fractional bit-plane coding ensures that thebitstream is embedded with fine granularity.

Since each sub-band is coded independently, the bitstream of eachsub-band is separable. The decoder 152 can easily extract only a fewsub-bands and decode only these sub-bands, making resolution scalabilityand temporal scalability natural and easy. According to the requirementof various multimedia applications, the final bitstream can beconstructed in an order to meet the requirement. To obtain resolution ortemporal (frame rate) scalability, for example, the bitstream can beassembled sub-band by sub-band, with the lower resolution or lowertemporal sub-band in the beginning. For seven sub-bands illustrated inFIG. 9, the four lower level sub-bands can be coded first, followed bythe three higher level sub-bands.

Moreover, the final bitstream can be rearranged to achieve otherscalability easily because the offset and the length of each layer ofbitstream from each sub-band are coded in the header of the bitstream.This property makes the final bitstream very flexible to be re-used forall sorts of applications without re-encoding again.

Conclusion

Although the description above uses language that is specific tostructural features and/or methodological acts, it is to be understoodthat the invention defined in the appended claims is not limited to thespecific features or acts described. Rather, the specific features andacts are disclosed as exemplary forms of implementing the invention.

1. A method comprising: forming a pixel array containing a current pixelin a current frame; determining whether a pixel corresponding to thecurrent pixel resides in a next frame subsequent to the current frame;if the corresponding pixel exists, add the current pixel to the pixelarray; and if the corresponding pixel does not exist, terminate thepixel array with the current pixel.
 2. A method as recited in claim 1,further comprising initially indicating all pixels as one state andsubsequently changing the state of each pixel after said determining ofthe pixel.
 3. A method as recited in claim 1, further comprisingapplying a wavelet transform to the pixel array.
 4. A method as recitedin claim 1, further comprising: applying a wavelet transform to thepixel array to produce wavelet coefficients; and applying a spatial 2-Dwavelet transform on the wavelet coefficients.
 5. A method as recited inclaim 1, further comprising: applying a 1 -D shape-adaptive discretewavelet transform to the pixel array to produce coefficients;redistributing the coefficients to corresponding spatial positions ineach frame; and applying a spatial 2-D wavelet transform on thecoefficients.
 6. A computer-readable medium comprisingcomputer-executable instructions that, when executed by one or moreprocessors, perform the method as recited in claim
 1. 7. A methodcomprising: estimating motion trajectories of pixels in a video objectfrom frame to frame in a video sequence; forming a pixel arraycontaining pixels that correspond to one another across multiple frames;and applying a wavelet transform to the pixel array.
 8. A method asrecited in claim 7, wherein the applying the wavelet transform to thepixel array produces wavelet coefficients and further comprising codingthe wavelet coefficients.
 9. A method as recited in claim 8, furthercomprising: coding the wavelet coefficients in bit-planes; andallocating bits for the bit-planes according to a rate-distortionoptimization.
 10. A method as recited in claim 7, wherein the applyingcomprises applying a 3-D wavelet transform to the pixel array.
 11. Amethod as recited in claim 7, wherein the applying comprises: applying a1-D shape-adaptive discrete wavelet transform to the pixel array toproduce coefficients; and applying a spatial 2-D wavelet transform tothe coefficients.
 12. A computer-readable medium comprisingcomputer-executable instructions that, when executed by one or moreprocessors, perform the method as recited in claim
 7. 13. A videoencoder comprising: a transformer to form a pixel array of pixels thatcorrespond to one another across multiple frames and to apply a wavelettransform to the pixel array to produce wavelet coefficients; and acoder to code the wavelet coefficients.
 14. A video encoder as recitedin claim 13, wherein the pixels fall along motion trajectories in atemporal direction from frame to frame.
 15. A video encoder as recitedin claim 13, wherein the wavelet transformer comprises a 3-D wavelettransformer.
 16. A video encoder as recited in claim 13, wherein thewavelet transformer comprises a temporal 1-D wavelet transform and aspatial 2-D wavelet transform.
 17. An operating system embodied on acomputer-readable medium comprising a video encoder as recited in claim13.
 18. A video encoder comprising: means for forming a pixel arraycontaining a current pixel in a current frame; means for determiningwhether a pixel corresponding to the current pixel resides in a nextframe subsequent to the current frame; and means for adding the currentpixel to the pixel array if the corresponding pixel exists and forterminating the pixel array with the current pixel if the correspondingpixel does not exist.
 19. A video encoder as recited in claim 18,further comprising means for applying a wavelet transform to the pixelarray.
 20. A video encoder as recited in claim 19, wherein the applyingmeans produces wavelet coefficients and further comprising means forcoding the wavelet coefficients.
 21. A video encoder as recited in claim18, further comprising: means for applying a 1-D shape-adaptive discretewavelet transform to the pixel array to produce coefficients; and meansfor applying a spatial 2-D wavelet transform to the coefficients.
 22. Anoperating system embodied on a computer-readable medium comprising avideo encoder as recited in claim
 18. 23. A video encoder comprising:means for estimating motion trajectories of pixels in a video objectfrom frame to frame in a video sequence; means for forming a pixel arraycontaining pixels that correspond to one another across multiple frames;and means for applying a wavelet transform to the pixel array.
 24. Avideo encoder as recited in claim 23, wherein the applying meansproduces wavelet coefficients and further comprising means for codingthe wavelet coefficients.
 25. A video encoder as recited in claim 24,wherein the coding means comprises: means for coding the waveletcoefficients in bit-planes; and means for allocating bits for thebit-planes according to a rate-distortion optimization.
 26. A videoencoder as recited in claim 24, wherein the applying means comprisesmeans for applying a 3-D wavelet transform to the pixel array.
 27. Avideo encoder as recited in claim 24, wherein the applying meanscomprises: means for applying a 1-D shape-adaptive discrete wavelettransform to the pixel array to produce coefficients; and means forapplying a spatial 2-D wavelet transform to the coefficients.
 28. Anoperating system embodied on a computer-readable medium comprising avideo encoder as recited in claim
 24. 29. A computer-readable mediumcomprising computer-executable instructions that, when executed on aprocessor, direct a device to: form a pixel array containing a currentpixel in a current frame; determine whether a pixel corresponding to thecurrent pixel resides in a next frame subsequent to the current frame;if the corresponding pixel exists, add the current pixel to the pixelarray; and if the corresponding pixel does not exist, terminate thepixel array with the current pixel.
 30. A computer-readable medium asrecited in claim 29, further comprising computer-executable instructionsthat, when executed on a processor, direct a device to apply a wavelettransform to the pixel array.
 31. A computer-readable medium as recitedin claim 29, further comprising computer-executable instructions that,when executed on a processor, direct a device to: apply a wavelettransform to the pixel array to produce wavelet coefficients; and applya spatial 2-D wavelet transform on the wavelet coefficients.
 32. Acomputer-readable medium as recited in claim 29, further comprisingcomputer-executable instructions that, when executed on a processor,direct a device to: apply a 1-D shape-adaptive discrete wavelettransform to the pixel array to produce coefficients; redistribute thecoefficients to corresponding spatial positions in each frame; and applya spatial 2-D wavelet transform on the coefficients.
 33. Acomputer-readable medium comprising computer-executable instructionsthat, when executed on a processor, direct a device to: estimate motiontrajectories of pixels in a video object from frame to frame in a videosequence; and form a pixel array containing pixels that correspond toone another across multiple frames.
 34. A computer-readable medium asrecited in claim 33, further comprising computer-executable instructionsthat, when executed on a processor, direct a device to apply a wavelettransform to the pixel array.
 35. A computer-readable medium as recitedin claim 33, further comprising computer-executable instructions that,when executed on a processor, direct a device to: apply a 1-Dshape-adaptive discrete wavelet transform to the pixel array to producecoefficients; and apply a spatial 2-D wavelet transform to thecoefficients.
 36. A computer-readable medium as recited in claim 33,further comprising computer-executable instructions that, when executedon a processor, direct a device to: apply a wavelet transform to thepixel array to produce wavelet coefficients; and code the waveletcoefficients.
 37. A computer-readable medium as recited in claim 33,further comprising computer-executable instructions that, when executedon a processor, direct a device to: apply a wavelet transform to thepixel array to produce wavelet coefficients; code the waveletcoefficients in bit-planes; and allocate bits for the bit-planesaccording to a rate-distortion optimization.